To reduce the volatility of returns in a portfolio, planners combine assets that tend to have low correlation to one another. There are many examples of the importance of low correlation. For example, a basketball team needs players with different attributes and talents—the team must be diversified. Building a basketball team with five point guards is not a great idea, as much as we value point guards. A center is needed, as well as several forwards. Because they have different attributes and talents, the correlation between point guards and power forwards is low-and low correlation is what we're after.

Low correlation equals diversification. Economics professor Harry Markowitz summarizes the basic premise underlying diversification and portfolio asset allocation in a simple sentence in Portfolio Selection: "To reduce risk, it is necessary to avoid a portfolio whose securities are all highly correlated with each other." It is assumed that Markowitz was equating the term "risk" with volatility of returns. In addition, financial theorist William Bernstein observed in The Intelligent Asset Allocator that "the concept of correlation of assets is central to portfolio theory—the lower the correlation, the better."

The maximum correlation between two parts of a system is +1.0 (or 100%), and the minimum correlation is -1.0 (or -100%). A correlation of +1.0 indicates that the behavior of the two parts is quite similar (i.e., two twin brothers who both play point guard). A correlation of -1.0 indicates that the two parts behave in oppositie manners (i.e., a left-handed 6'1" point guard and a right-handed 7'4" center). A correlation of zero indicates that the relationship between the behavior of the two parts is basically random.

As it pertains to investment portfolios, correlation between two assets within a portfolio is measured in the range of -1.0 to +1.0, where -1.0 indicates that the price movement of two assets is perfectly inversely related. When one goes up, the other goes down, and vice versa. A coefficient of zero indicates no correlation between the assets, while a coefficient of +1.0 indicates perfect positive correlation. When one goes up, the other goes up.

The correlation goal for a multi-asset portfolio is zero. That goal means that the average correlation between all the assets in the portfolio should hover near zero. It's difficult to achieve consistently in actual practice, but we need to have a stated goal. A more pragmatic goal would be to build a portfolio in which the aggregate correlation among all the various assets is in the range of 0.30 to 0.40.

Interestingly, many of the asset classes that we tend to think of as "hedges" to large domestic equity—small-cap equity, non-U.S. equity, real estate and even commodities to a certain extent—have recently been more positively correlated. Cash and bonds remain better choices for diversification, but correlation is not the only key to a successful portfolio. The trick is to balance correlation and performance, while remembering that correlation is not a static number but one that changes over time.

CORRELATION PATTERNS

This article examines the patterns of correlation between seven core investment asset classes: large U.S. equities, small U.S. equities, non-U.S. equities, bonds, cash, real estate investment trusts (REITs) and commodities. These seven assets have performance histories that go back to 1970. This article examines the most recent 20-year period from Jan. 1, 1989, to Dec. 31, 2008.

Here are the indexes that were used as a proxy for each asset class:

• Large-cap U.S. equities: S&P 500 Index
• Small-cap U.S. equities: Russell 2000 Index
• Non-U.S. equities: Morgan Stanley Capital International EAFE Index (Europe, Australasia, Far East) Index
• U.S. intermediate-term bonds: Lehman Brothers Intermediate Government Bond Index (now the Barclays Capital Intermediate Govt. Bond Index)
• Cash: 3-month Treasury bills
• Real estate: Dow Jones Wilshire REIT Index
• Commodities: Goldman Sachs Commodities Index (GSCI). As of Feb. 6, 2007, the GSCI became known as the S&P GSCI.

Let's assume that the core asset class in most accumulation portfolios (that is, portfolios of individuals who are preparing for retirement) is large-cap U.S. stocks, specifically large-cap U.S. mutual funds. In order to achieve a diversified overall investment portfolio, we need to find several other assets that are different from U.S. large-cap funds. A common next step is to add small-cap U.S. stocks to diversify the large-cap stock-based portfolio.

That's a fine idea because of the long-term performance advantage of small caps. But unfortunately, adding small-cap stock funds to large-cap funds does not produce the level of diversification needed. Over the 20-year period from Jan. 1, 1989 to Dec. 31, 2008, the average correlation between large-cap and small-cap U.S. stocks averaged .76 and never strayed too far from that number. However, in recent years the correlation of rolling 12-month returns has been at or above 0.80. During the year of 2008, the correlation between the two was 0.96.